In a medium saucepan, whisk together egg yolks and 3/4 cup of sugar until well blended. Then, whisk in 2/3 cup eggnog and milk. Cook over medium heat, stirring constantly until boiling. Boil for one minute and remove from heat and cool slightly. Whisk in mascarpone cheese and let chill for 1 hour. In a chilled bowl, beat the cream, 1/4 cup sugar, and vanilla until soft peaks have formed. Put remaining 1 1/3 cups eggnog in a bowl. Dip each ladyfinger into eggnog until soaked. Place 1 layer of ladyfingers in the bottom of a 9×13 pan. Spread half of the mascarpone mixture on top then half of the whipped cream mixture next. Repeat layers. Sprinkle with chocolate shavings. Cover and refrigerate overnight.